Question

What is the effect on the graph of the function f(x) =|x| when f(x) is changed to f(4x).

Answer 1

When the function f(x) changed to f(kx), that means the function is compressed or stretched horizontally by a scale factor

If k > 1, then it is compressed horizontally by a scale factor of 1/k

If 0 < k < 1, then it is stretched horizontally by a scale factor of k

Since the given function is

$f(x)=\lvert x\rvert$

Since f(x) changed to

$f(4x)$

That means x is multiplied by 4

$f(4x)=\lvert4x\rvert$

The value of k = 4 and it is compressed/stretched horizontally

Since k = 4, then

k > 1 (by using the rule above)

Then f(x) is compressed horizontally by a scale factor of 1/4